One way of obtaining the large-scale poloidal magnetic flux near the BH is advecting it from large radii. While for geometrically thick discs this is expected to readily happen over short distances (as confirmed by 3D GRMHD simulations, e.g., [1]}, [2]}), it is unclear whether an accretion disc is capable of dragging in the poloidal flux from the ambient medium over 5–6 orders of magnitude in distance all the way down to the BH. This is particularly uncertain given that in many systems the accretion discs at large radii are expected to cool radiatively and become geometrically-thin.
In such discs the poloidal magnetic flux may diffuse out faster than it can be advected inwards ([3]}; however, inward transport of the magnetic flux by disc surface layers might help in alleviating this problem, [4]}, [5]}, [6]}).
